Combining Texts

Ideas for 'Parmenides', 'Regressive Method for Premises in Mathematics' and 'The Theory of Communicative Action'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

---

2 ideas

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

16150	One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]
	Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it.
	From: Plato (Parmenides [c.364 BCE], 144a)
	A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

17628	Arithmetic was probably inferred from relationships between physical objects [Russell]
	Full Idea: When 2 + 2 =4 was first discovered, it was probably inferred from the case of sheep and other concrete cases.
	From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.272)